The following courses are already available within the consortium. Interested students are encouraged to contact teachers and ask about possibilities to follow the course. Many courses will be available in a digital form.

#### Frontier in Material Sciencee

**Coordinator**: Dr. O. Chibykalo-Fesenko

**Next edition**: April 2021

**Description**: https://wp.icmm.csic.es/fronteras/

**Language**: English

#### Physics and Mathematics of Topological and Geometrical Effects

**Coordinator:** Prof. Dr. Y. Mokrousov

**Next editions**: October 2020-February 2021 and April 2021 – July 2021

**Description:**

The physics and required mathematical background of geometrical and topological phases in non-relativistic quantum physics are discussed in depth.

The course seeks to maintain a balance between presenting mathematical background uncommon to most physicists with profound physical applications.

The course aims to be self-contained and requires basic knowledge of mathematics and band theory of solids. The mathematics part of the lecture is a broad introduction to topology and differential geometry of manifolds, fibre bundle theory, characteristic classes and gauge theories. The physics part of the course is dedicated to selected aspects of geometry and topology in solid state physics, mathematical foundations of the Berry, or, geometric phase, considerations of the adiabatic and non-adiabatic dynamics of quantum systems, and discussion of fundamental aspects of the Berry connection, Berry

curvature, gauge freedom, parallel transportation and topological numbers. Practical examples are taken from the fields of electric polarization, topological insulators, skyrmions, and magnetization dynamics. The course can be followed from the beginning to the end with minimal reference to other sources.

**Language**: English

#### Density Functional Theory and Electronic Structure

**Coordinator:** Prof. Dr. S. Bluegel

**Next editions:** Oct-2020 – Feb-2021 (14 teaching weeks , 4 class hours per week + 2 tutorial hours in the computer lab. The next term the lectures will be ZOOM lectures.

**Description:**

The lecture introduces the foundations of density functional theory, the Hohenberg-Kohn theorem and the Kohn-Sham equations, and discusses different approximations for the exchange-correlation energy functional and their accuracy for calculating bond length in molecules and lattice structures in solids. The course is geared towards magnetism and spintronics and therefore topics are included relevant to theses fields. Thus, the course covers relativistic corrections, the mapping of the ab-initio total energies to model Hamiltonians to e.g. extract the finite temperature magnetic properties, spin-dependent transport phenomena and methods beyond the conventional exchange correlation approximations, such as LDA+U or Hubbard I approximation. Different extensions on DFT will be discussed e.g. time-dependent density functional theory or many-body perturbation theory in the GW approximation of Hedin. The DFT is realized in so-called quantum engines, i.e. electronic structure codes realising different electronic structure methods. Different possibilities of the computational implementation of DFT are introduced. An important aspect of the lecture is the exercise which takes the partly the form of a tutorial. Some of which are used in hands-on exercises and tutorial to calculate e.g. Lattice constants, lattice structures, surface properties like surface energy and work functions, density of states and band structures of solids, local magnetic moments, magnetic exchange interactions and magnetic anisotropy andnon-collinear magnetic structures such as spin spirals. In this practical part of the lecture, we will employ the full-potential linearized augmented planewave method (FLAPW)-based code FLEUR.

#### The Physics of Nanoelectronic Systems

**Coordinator**: Dr. C. Ciccarelli

**Description**: Course page.

#### Non-linear optics and Quantum States of Light

**Coordinator**: Dr. C. Ciccarelli

**Description**: Course page.

#### NanoSpintronics

Course offered in form of four 4-hour lectures in week 1 and 2, the rest of the weeks is for modelling projects and guest lectures.

**Coordinator**: Prof. Dr. B. Koopmans

**Next edition**: Quartile 4 of each academic year (typically mid-April to end of June)

**Description**: Course page

#### NanoMagnetism

Parallel to the introduction of conceptual knowledge, the students will work on practical tasks during instructions and experimental sessions in the research laboratory.

**Coordinator**: Dr. R. Lavrijsen

**Next edition:** Quartile 2 of each academic year (typically November to half of January)

**Description**: Course page

#### Laser-matter interaction

**Coordinator**: Prof. Dr. A. V. Kimel

**Next edition**: Quartile 3-4 of each academic year (typically February-June)

**Description**: Course page

#### Fundamentals of Magnetism

**Coordinator**: Prof. Dr. A. Kirilyuk

**Next edition**: Quartile 3-4 of each academic year (typically February-June)

**Description**: Course page